Timing-aware test generation and fault simulation

ABSTRACT

Disclosed herein are exemplary methods, apparatus, and systems for performing timing-aware automatic test pattern generation (ATPG) that can be used, for example, to improve the quality of a test set generated for detecting delay defects or holding time defects. In certain embodiments, timing information derived from various sources (e.g. from Standard Delay Format (SDF) files) is integrated into an ATPG tool. The timing information can be used to guide the test generator to detect the faults through certain paths (e.g., paths having a selected length, or range of lengths, such as the longest or shortest paths). To avoid propagating the faults through similar paths repeatedly, a weighted random method can be used to improve the path coverage during test generation. Experimental results show that significant test quality improvement can be achieved when applying embodiments of timing-aware ATPG to industrial designs.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of Ser. No. 14/803,866 filed Jul. 20,2015, which is a divisional of U.S. patent application Ser. No.14/053,322, filed Oct. 14, 2013, now U.S. Pat. No. 9,086,454, which is adivisional of U.S. patent application Ser. No. 13/285,899, filed Oct.31, 2011, now U.S. Pat. No. 8,560,906, which is a divisional of U.S.patent application Ser. No. 11/796,374, filed Apr. 27, 2007, now U.S.Pat. No. 8,051,352, which claims the benefit of U.S. Provisional PatentApplication No. 60/796,212, filed Apr. 27, 2006, and U.S. ProvisionalPatent Application No. 60/859,634, filed Nov. 18, 2006, all of which arehereby incorporated herein by reference.

FIELD

This application relates generally to the field of generating testpatterns for testing integrated circuits.

BACKGROUND

To verify the correct operation of manufactured circuits, it isdesirable for the circuits not only to have correct functional behavior,but also to operate correctly at a certain clock frequency (e.g., theoperational clock frequency). As logic circuits operate at higherfrequencies and as feature sizes shrink, manufactured circuits becomemore vulnerable to timing-related defects.

Delay fault testing has therefore become a desirable part of integratedcircuit testing and can be used to help achieve high test quality.Delay-related defects typically originate from process variations andrandom defects. Process variations are ordinarily caused by physicalparameter variations during the manufacturing process and usually cannotbe completely eliminated. Tightly controlling the process variations andadding extra delay margins during the design phase are two commonmethods to help tolerate process variations. Random delay defects,caused for example by resistive shorts and resistive vias, introduceadditional delays and may also cause circuits to malfunction duringnormal operation.

Various fault models have been proposed to target delay defects. Thetransition fault model, for instance, considers a gross delay at everygate terminal in the circuit and assumes that the additional delay atthe fault site is large enough to cause a logic failure. See, e.g., J.A. Waicukauski, E. Lindbloom, B. K. Rosen, and V. S. Iyengar,“Transition Fault Simulation,” IEEE Design & Test of Computer, pp. 32-38(April 1987). Due to the limited fault population with the transitionfault model, the model has been widely used in industry. However,transition fault test generation generally ignores the actual delaysthrough the fault activation and propagation paths, and is more likelyto detect a fault through a shorter path. As a result, the generatedtest set may not be capable of detecting small delay defects.

To improve the quality of delay defect test sets such that small delaydefects can be detected, it is desirable to integrate timing informationinto one or more stages of the test generation process.

SUMMARY

Disclosed herein are exemplary methods, apparatus, and systems forperforming timing-aware automatic test pattern generation (ATPG) thatcan be used, for example, to improve the quality of a test set generatedfor detecting delay defects. In certain embodiments, timing informationderived from various sources (e.g. from Standard Delay Format (SDF)files) is integrated into an ATPG tool. The timing information can beused to guide the test generator to detect the faults through certainpaths (e.g., paths having a selected length, or range of lengths, suchas the longest paths). To avoid propagating the faults through similarpaths repeatedly, a weighted random method can be used to improve thepath coverage during test generation. Experimental results show thatsignificant test quality improvement can be achieved when applyingembodiments of timing-aware ATPG to industrial designs.

Among the features and aspects that can be used alone or in variouscombinations and subcombinations with each other in embodiments of thedisclosed technology are the following:

A fault dropping method to determine if the fault should be removed fromthe test generation target list so that the testable faults are detectedthrough the longest (or other desirably long) sensitized path. Incertain implementations, for instance, the fault drop criterion is whenthe fault is observed by at least one of the observation points and theslack margin is not larger than a user-specified amount. In someembodiments, the fault drop criterion is when the fault is observed byat least one of the observation points and the slack margin is equal tozero. In other embodiments, the fault drop criterion is when the faultis observed by at least one of the observation points and the slack isnot larger than a minimum static slack set by a user-specified number.

A static timing simulation method to compute the arrival time,propagation time, and slack of each pin for an integrated circuit design(e.g., a circuit design with multiple clock frequencies, a design withcombinational feedback loops, a design with false paths and multi-cyclepaths, or other such design).

A fault-independent timing fault simulation method that computes theactual minimum slack of detected faults of a given pattern (e.g., for acircuit design with multiple clock frequencies, combinational feedbackloop, false paths, and/or multi-cycle paths).

A test generation method that detects small delay defects by launching adelay fault (e.g., a transition fault) through one of the sensitizablepaths to the faulty site selected by using a weighted randomjustification decision, and propagating the fault from the faulty siteto one of the sensitizable observation points selected by using aweighted random propagation decision. In certain embodiments, theweighted justification decision depends on the static arrival time of agate input, such that the input with the longer arrival time contains alarger weight and has a higher probability of being selected as part ofthe justification path. In some embodiments, the weighted propagationdecision can depend on the static propagation time of the gate fanout,such that the fanout gate with the longer propagation time contains alarger weight and has a higher probability of being selected as part ofthe propagation path.

A test generation method for the transition fault model that detectssmall delay defects by launching the fault through one of thesensitizable paths to the faulty site selected by using a deterministicjustification decision, and propagating the fault from the faulty siteto one of the sensitizable observation points selected by using adeterministic propagation decision. The deterministic justificationdecision can depend on the static arrival time of the gate input, and/oron the static propagation time of the gate fanout.

For any of the embodiments, a path delay fault model that does notexplicitly enumerate a path can also be used. Instead, the model canimplicitly derive the path while performing the test generation and, forexample, ensure that one or multiple of the longest (or other desirablylong) sensitization paths through the pins are detected. Further, forany of the embodiments, any suitable fault model (such as the as late aspossible transition fault (ALAPTF) model) can be used.

In one exemplary embodiment described herein, two or more possible faultpropagation paths in an integrated circuit design are identified. Thepossible fault propagation paths are capable of propagating a faulteffect of a targeted delay fault to an observation point in theintegrated circuit design. One of the possible fault propagation pathsis selected using a weighted random selection procedure. Test patternvalues are generated that propagate the fault effect on the selectedfault propagation path. The test pattern values can be stored. In someimplementations, the weighted random selection procedure favors faultpropagation paths with longer path delays over fault propagation pathswith shorter path delays. In other implementations, the weighted randomselection procedure favors fault propagation paths with shorter pathdelays over fault propagation paths with longer path delays. In certainimplementations, weights are computed for each of the possible faultpropagation paths. For example, the computed weight for a respective oneof the possible fault propagation paths can indicate the probabilitythat the respective one of the possible fault propagation paths will beselected by the weighted random selection procedure. In particularexamples, a weight w_(i) for a respective possible fault propagationpath i is computed as follows:

${w_{i} = \frac{{PT}_{i}^{s}}{\sum\limits_{i = 1}^{n}{PT}_{i}^{s}}},$where n is the number of possible fault propagation paths, i is an indexvalue, and PT_(i) ^(s) is the longest static propagation time for thepossible fault propagation path i. In other particular examples, aweight w_(i) for a respective possible fault propagation path i iscomputed as follows:

${w_{i} = \frac{\frac{1}{{HPT}_{i}^{s}}}{\sum\limits_{i = 1}^{n}\frac{1}{{HPT}_{i}^{s}}}},$where n is the number of possible fault propagation paths, i is an indexvalue, and HPT_(i) ^(s) is the shortest static propagation time for thepossible fault propagation path i. In certain embodiments, propagationtimes are computed for one or more gates in the possible faultpropagation paths, and the weighted random selection procedure is basedat least in part on the computed propagation times. In certain examples,timing information from an SDF file can be used. In certainimplementations, a fault activation condition for activating thetargeted delay fault is selected using a weighted random selectionprocedure that favors fault activation conditions having longer arrivaltimes over fault activation conditions having shorter arrival times. Inother implementations, a fault activation condition for activating thetargeted delay fault is selected using a weighted random selectionprocedure that favors fault activation conditions having shorter arrivaltimes over fault activation conditions having longer arrival times.

In another embodiment described herein, two or more possible faultactivation conditions in an integrated circuit design are identified.The possible fault activation conditions are capable of activating atargeted delay fault at a fault site through a gate in the integratedcircuit design. One of the possible fault activation conditions isselected using a weighted random selection procedure. Test patternvalues are generated that activate the targeted delay fault at the faultsite with the selected fault activation conditions. The test patternvalues can be stored. In some implementations, the weighted random pathselection procedure favors paths with longer arrival times to thetargeted delay fault site over paths with shorter arrival times to thetargeted delay fault site. In other implementations, the path selectionprocedure favors paths with shorter arrival times to the targeted delayfault site over paths with longer arrival times to the targeted delayfault site. In particular implementations, weights are computed for eachof the possible fault activation conditions. For example, the computedweight for a respective one of the possible fault activation conditionscan indicate the probability that the respective one of the possiblefault activation conditions will be selected by the weighted randomselection procedure. In a particular example, a weight w_(i) for arespective possible fault activation condition i is computed as follows:

${w_{i} = \frac{{AT}_{i}^{s}}{\sum\limits_{i = 1}^{n}{AT}_{i}^{s}}},$where n is the number of possible fault activation conditions, i is anindex value, and AT_(i) ^(s) is the longest static arrival time to theith choice to justify the gate. In another particular example, a weightw_(i) for a respective possible fault activation condition i is computedas follows:

${w_{i} = \frac{\frac{1}{{HAT}_{i}^{s}}}{\sum\limits_{i = 1}^{n}\frac{1}{{HAT}_{i}^{s}}}},$where n is the number of possible fault activation conditions, i is anindex value, and HAT_(i) ^(s) is the shortest static arrival time to theith choice to justify the gate. In certain implementations, activationtimes for one or more gates in the paths used with the possible faultactivation conditions are computed, and the weighted random selectionprocedure is based at least in part on the computed activation times.The act of computing the activation times can comprise using timinginformation from an SDF file. In some implementations, a faultpropagation path is selected for propagating a fault effect of thetargeted delay fault to an observation point of the integrated circuitdesign using a weighted random selection procedure that favors faultpropagation paths having longer propagation times over fault propagationpaths having shorter propagation times. In other implementations, afault propagation path is selected for propagating a fault effect of thetargeted delay fault to an observation point of the integrated circuitdesign using a weighted random selection procedure that favors faultpropagation paths having shorter propagation times over faultpropagation paths having longer propagation times.

In another embodiment disclosed herein, a fault that is detected by atest pattern is identified by simulating a response of an integratedcircuit design to the test pattern in the presence of the fault andidentifying one or more paths that are sensitized by the test patternand that detect the fault. An actual path delay for the identified faultis computed. A determination is made that the identified fault is to beremoved from a fault list, the determination being based at least inpart on the computed actual path delay. The fault list is modified byremoving the identified fault. The modified fault list can be stored. Insome implementations, the determination is further based at least inpart on the static path delay. For example, in certain implementations,the determination is based at least in part on a relative differencebetween actual slack and static slack of the longest sensitized pathdetecting the fault, the actual slack being determined by the actualpath delay through the longest sensitized path detecting the fault andthe static slack being determined by the static path delay through thelongest sensitized path detecting the fault. In certain implementations,the determination is made by determining that the following condition ismet:

${\frac{{PD}_{f}^{s} - {PD}_{f}^{a}}{T_{TC} - {PD}_{f}^{a}} < \delta},$where PD_(f) ^(s) is the static path delay for the fault f, PD_(f) ^(a)is the actual path delay for the fault, T_(TC) is the test clock period,and δ is a real number between 0 and 1 and can be user-selectable. Inother implementations, the determination is based at least in part on arelative difference between actual slack and static slack of theshortest sensitized path detecting the fault, the actual slack beingdetermined by the actual path delay through the shortest sensitized pathdetecting the fault and the static slack being determined by the staticpath delay through the shortest sensitized path detecting the fault. Incertain implementations, the determination can include determining thatthe following condition is met:

${\frac{{HPD}_{f}^{a} - {HPD}_{f}^{s}}{T_{TC} - {HPD}_{f}^{s}} < \delta},$where HPD_(f) ^(s) is the static path delay through the shortestsensitized path for the fault f, HPD_(f) ^(a) is the actual path delaythrough the shortest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and 1 and can beuser-selectable. In particular implementations, the method is repeatedfor additional faults in the fault list not detected by previouslygenerated test patterns. In some implementations, a good machinesimulation is performed to determine a response of the integratedcircuit design to the test pattern in the absence of any faults, and oneor more paths sensitized by the test pattern are identified.

In another disclosed embodiment, a fault that is detected by a testpattern is identified by simulating a response of an integrated circuitdesign to the test pattern in the presence of the fault and identifyingone or more paths that are sensitized by the test pattern and thatdetect the fault. A static path delay is computed for a selectedsensitized path through the identified fault. A determination is made asto whether a criterion based at least in part on the static path delayis met for the identified fault. The fault list is modified by removingthe identified fault if the criterion is met. The modified fault listcan be stored. In particular implementations, the selected sensitizedpath is the longest sensitized path. For example, in certain exemplaryimplementations, the determination includes determining whether:

$\frac{T_{TC} - {PD}_{f}^{s}}{T_{TC}} \geq \lambda$where PD_(f) ^(s) is the static path delay through the longestsensitized path for the fault f, T_(TC) is the test clock period, and λis a real number between 0 and 1. In other implementations, the selectedsensitized path is the shortest sensitized path. For example, in certainexemplary implementations, the determination includes determiningwhether:

$\frac{T_{TC} - {HPD}_{f}^{s}}{T_{TC}} < \lambda$where HPD_(f) ^(s) is the static path delay through the shortestsensitized path for the fault f, T_(TC) is the test clock period, and λis a real number between 0 and 1. In particular implementations, thecriterion is a first criterion, and the method further comprisescomputing an actual path delay for the selected sensitized path throughthe identified fault, determining whether a second criterion based atleast in part on the actual path delay is met for the identified fault,and modifying the fault list by removing the identified fault if thefirst criterion is not met but the second criterion is met. In oneexample, the act of determining whether the second criterion is metcomprises determining whether:

${\frac{{PD}_{f}^{s} - {PD}_{f}^{a}}{T_{TC} - {PD}_{f}^{a}} < \delta},$where PD_(f) ^(s) is the static path delay through the longestsensitized path for the fault f, PD_(f) ^(a) is the actual path delaythrough the longest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and 1. In anotherexample, the act of determining whether the second criterion is metcomprises determining whether:

${\frac{{HPD}_{f}^{a} - {HPD}_{f}^{s}}{T_{TC} - {HPD}_{f}^{s}} < \delta},$where HPD_(f) ^(s) is the static path delay through the shortestsensitized path for the fault f, HPD_(f) ^(a) is the actual path delaythrough the shortest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and 1. The method can berepeated for additional faults in the fault list not detected bypreviously generated test patterns.

In another disclosed embodiment, a response of an integrated circuitdesign to a test pattern is simulated in the absence of any faults inthe integrated circuit design. Paths sensitized by the test pattern areidentified by backward tracing from the observation points of theintegrated circuit design and analyzing sensitization conditions in theintegrated circuit design (including, for example, reconvergent pathsensitization conditions). A fault detected by the test pattern isidentified by simulating a response of the integrated circuit design tothe test pattern in the presence of the fault and determining that oneor more of the identified paths detect the fault. A path delay for theone or more paths that detect the fault is determined. The path delaycan be stored. In particular implementations, the path delay is computedusing the longest propagation time in the identified paths. In otherimplementations, the path delay is computed suing the shortestpropagation time in the identified paths. In certain implementations,the path delay is a current path delay, and the act of storing the pathdelay comprises comparing the current path delay to a previously storedpath delay associated with the fault, and replacing the previouslystored path delay with the current path delay if the current path delayis longer. In other implementations, the path delay is a current pathdelay, and the act of storing the path delay comprises comparing thecurrent path delay to a previously stored path delay associated with thefault, and replacing the previously stored path delay with the currentpath delay if the current path delay is shorter. In someimplementations, the path delay is the actual path delay. In theseimplementations, an actual slack time using the actual path delay can becomputed, and the fault can be removed from a fault list if auser-selected criterion based at least in part on the actual slack timeis met. Further, in particular implementations, the act of identifyingpaths comprises identifying reconvergent sensitization paths.

Any of the disclosed methods can be implemented as computer-readablemedia comprising computer-executable instructions for causing a computerto perform the methods. Any of the disclosed methods implemented in acomputer environment can also be performed by a single computer or via anetwork. Further, computer-readable media storing test patterns or testpattern values (or any other final or intermediate results) produced byany of the disclosed methods are also disclosed.

The foregoing and other objects, features, and advantages of theinvention will become more apparent from the following detaileddescription, which proceeds with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram illustrating how the delay on a pathcan impact the size of the defect delay that is detectable on the path.

FIG. 2 is a schematic block diagram of a circuit portion illustratinghow embodiments of the disclosed technology can identify reconvergentsensitization paths.

FIG. 3 is a graph illustrating types of delay defects that may not bedetectable for a given path delay.

FIG. 4 is a flowchart of an exemplary method of performing timing-awaretest pattern generation.

FIG. 5 is a flowchart of an exemplary method for determining propagationpaths as can be used in the timing-aware test pattern generation methodof FIG. 4.

FIG. 6 is a schematic block diagram illustrating the propagation pathselection method of FIG. 5.

FIG. 7 is a flowchart of an exemplary method for determining faultactivation conditions as can be used in the timing-aware test patterngeneration method of FIG. 4.

FIG. 8 is a schematic block diagram illustrating the fault activationcondition selection method of FIG. 7.

FIG. 9 is a flowchart of an exemplary method for performing timing-awarefault simulation.

FIG. 10 is a schematic block diagram illustrating the exemplary faultsimulation method of FIG. 9.

FIG. 11 is a flowchart of an exemplary timing-aware fault droppingmethod as can be used in any of the disclosed embodiments.

FIG. 12 is a first graph reporting experimental results. The graph inFIG. 12 shows the distribution of differences between static and actualpath delays for traditional ATPG.

FIG. 13 is a second graph reporting experimental results. The graph inFIG. 13 shows results from a conventional ATPG method and an exemplaryembodiment of timing-aware ATPG with N=1.

FIG. 14 is a third graph reporting experimental results. The graph inFIG. 14 shows results from a conventional ATPG method and an exemplaryembodiment of timing-aware ATPG with N=20.

FIG. 15 is a fourth graph reporting experimental results. The graph inFIG. 15 shows results from a conventional ATPG method and an exemplaryembodiment of timing-aware ATPG with DSM=0.5.

FIG. 16 is a graph showing distributions of example timing criticaltransition faults with different λ for four industrial designs.

FIG. 17 is a flowchart of an exemplary timing-aware deterministic testgeneration procedure that includes multiple fault dropping criteria.

FIG. 18 is a schematic block diagram of a network as may be used togenerate test patterns according to any of the disclosed embodiments.

FIG. 19 is a schematic block diagram of a distributed computing networkas may be used to generate test patterns according to any of thedisclosed embodiments.

FIG. 20 is a flowchart illustrating how test patterns can be generatedusing the networks of FIG. 18 or FIG. 19.

DETAILED DESCRIPTION

General Considerations

Disclosed herein are exemplary methods, apparatus, and systems forperforming timing-aware ATPG, which can be used, for example, to improvethe quality of a test set generated for detecting delay defects. Thedisclosed methods, apparatus, and systems should not be construed aslimiting in any way. Instead, the present disclosure is directed towardall novel and nonobvious features and aspects of the various disclosedmethods, apparatus, systems, and equivalents thereof, alone and invarious combinations and subcombinations with one another. The presentdisclosure is not limited to any specific aspect or feature, orcombination thereof, nor do the disclosed methods, apparatus, andsystems require that any one or more specific advantages be present orproblems be solved.

Although the operations of some of the disclosed methods, apparatus, andsystems are described in a particular, sequential order for convenientpresentation, it should be understood that this manner of descriptionencompasses rearrangement, unless a particular ordering is required byspecific language set forth below. For example, operations describedsequentially may in some cases be rearranged or performed concurrently.Moreover, for the sake of simplicity, the attached figures may not showthe various ways in which the disclosed methods, apparatus, and systemscan be used in conjunction with other methods, apparatus, and systems.Additionally, the description sometimes uses terms like “identify” and“determine” to describe the disclosed methods. These terms arehigh-level abstractions of the actual operations that are performed. Theactual operations that correspond to these terms will vary depending onthe particular implementation and are readily discernible by one ofordinary skill in the art.

The disclosed embodiments can be used to generate test patterns fortesting a wide variety of scan-based or partially-scan-based circuits(for example, application-specific integrated circuits (ASICs)(including mixed-signal ASICs), systems-on-a-chip (SoCs), orprogrammable logic devices (PLDs), such as field programmable gatearrays (FPGAs)). Any of the methods or techniques described herein canbe performed using software that comprises computer-executableinstructions for causing a computer to perform the methods or techniquesstored on one or more computer-readable media. Such software cancomprise, for example, an electronic-design-automation (EDA) softwaretool, such as an ATPG tool. Any such software can be executed on asingle computer or on a networked computer system (for example, via theInternet, a wide-area network, a local-area network, a client-servernetwork, or other such network). For clarity, only certain selectedaspects of the software-based implementations are described. Otherdetails that are well known in the art are omitted. For example, itshould be understood that the disclosed technology is not limited to anyspecific computer language, program, or computer and that the disclosedtechnology can be implemented using any commercially available computer.For the same reason, computer hardware is not described in furtherdetail.

One or more test patterns or intermediate results produced by any of thedisclosed methods, apparatus, and systems can also be stored on one ormore computer-readable media as part of the described ATPG methods andtechniques and are considered to be within the scope of this disclosure.Computer-readable media storing such test patterns or intermediateresults may be accessed and used by a single computer, networkedcomputer (such as those described above), or dedicated testing system(for example, a tester or automatic testing equipment (ATE)).

Any of the disclosed methods can be used to generate test patterns in acomputer simulation environment wherein test patterns are generated forrepresentations of circuits, which are stored on one or morecomputer-readable media. For example, the disclosed methods typicallyuse circuit design information (for example, a netlist, HDL description(such as a Verilog or VHDL description), GDSII description, or the like)stored on computer-readable media. For presentation purposes, however,the present disclosure sometimes refers to the circuit and its circuitcomponents by their physical counterpart (for example, gates, primaryoutputs, paths, and other such terms). It should be understood, however,that any such reference not only includes the physical components butalso representations of such circuit components as are used insimulation, ATPG, or other such EDA environments.

As used in this disclosure and the claims, the singular forms “a,” “an,”and “the” include the plural forms unless the context clearly dictatesotherwise. Additionally, the term “includes” means “comprises.”

Further, certain aspects of the disclosed technology involve storing orretrieving data from one or more lists. As used herein, the term “list”refers to a collection or arrangement of data that is usable by acomputer. A list may be, for example, a data structure or combination ofdata structures (such as a queue, stack, array, linked list, heap, ortree) that organizes data for better processing efficiency, or any otherstructured logical or physical representation of data in a computersystem or computer-readable media (such as a table used in a relationaldatabase). Moreover, any of the lists discussed herein may be persistent(that is, the list may be stored in computer-readable media such that itis available beyond the execution of the application creating and usingthe list) or non-persistent (that is, the list may be only temporarilystored in computer-readable media such that it is cleared when theapplication creating and using the list is closed or when the list is nolonger needed by the application).

Furthermore, the disclosed embodiments can be used in connection withany suitable delay defect fault model. For example, any known or newlydeveloped delay defect fault model can be used with the disclosedembodiments (e.g., the transition fault model or the as late as possibletransition fault (ALAPTF) model described in P. Gupta and M. S. Hsiao,“ALAPTF: A New Transition Fault Model and the ATPG Algorithm,” Proc. ITC2004, pp. 1053-1060).

Introduction to Disclosed Technology

Embodiments of the disclosed technology integrate timing information(e.g., I/O path and interconnect delay information from SDF files) intothe test generation process. In exemplary embodiments, the transitionfault model is adopted, since it is applicable to large industrialdesigns. It should be understood, however, that other fault models maybe used depending on the implementation. Among the various aspects ofthe disclosed technology that may be realized alone or in variouscombinations or subcombinations with one another are the following:

Timing information can be applied during the test generation process. Insome embodiments, timing information is applied to guide faultpropagation. For example, timing information can be used to propagatethe fault effect to a primary output (e.g., an output pin) or pseudoprimary output (e.g., an input of a scan cell) through a selectedsensitization path (e.g., the longest or other desirably longsensitization path). In some embodiments, timing information is appliedto guide fault activation. For example, timing information can be usedto launch the transition at a fault site from a primary input (e.g., aninput pin) or a pseudo-primary input (e.g., an output of a scan cell)through the longest (or other desirably long) path. In certain desirableembodiments, timing information is used to guide both fault propagationand fault activation.

Timing information can also be applied during the fault simulationprocess. In certain embodiments, for example, timing information isapplied to calculate the fault effect propagation time from thetransition fault site to an observation point and to calculate thetransition arrival time to the transition fault site from primary inputsor pseudo-primary inputs.

Fault dropping criteria can also be used during test generation. Forexample, in certain embodiments, one or more of the following criteriaare used: test generation effort, test pattern count, and/or testquality of the delay defects. In certain desirable embodiments, acriteria based on actual path delay of a sensitized path detecting afault is used to determine whether a fault is to be dropped. In otherdesirable embodiments, a criterion based on both static path delay andactual path delay of a sensitized path detecting a fault is used todetermine whether a fault is to be dropped.

The resulting test patterns can be evaluated using test quality metrics.For example, test quality can be evaluated by applying both delay testcoverage and statistical delay quality level (SDQL) metrics.

Detecting Delay Defects

Depending on the size of a delay defect, the extra delay caused by thedefect may not impact all of the paths passing though the delay faultsite. For example, shorter paths typically have larger slack marginsthan longer paths and can tolerate additional delay. Consider, forexample, the schematic block diagram 100 shown in FIG. 1. Block diagram100 shows a clock waveform 110 relative to the path delays 120, 122, 124of three exemplary paths P₁, P₂, P₃ on which a given fault can bedetected. Path P₁ has the longest path delay of 9.5 ns, path P₂ has apath delay of 7.5 ns, and path P₃ has a path delay of 7.0 ns. Assumethat the clock period of the clock waveform 110 is 10 ns. Consequently,the slacks for the paths P₁, P₂, P₃ (the difference between the systemclock period and the path delay) are 0.5 ns, 2.5 ns, and 3 ns,respectively. In general, the smallest defect delay that can be detectedon a given path is equal to the slack of the path. For example, on pathP₁, the smallest defect delay that can be detected is 0.5 ns, because0.5 ns+9.5 ns=10 ns (the clock period). A defect delay greater than 0.5ns will cause the path P₁ to fail, as the delay will be greater than thesystem clock period. The delay defect will therefore be detected on thepath. By contrast, a defect delay of 0.5 ns will not be detected on thepaths P₂, P₃. Accordingly, it is desirable to select longer paths forfault propagation and fault activation during the test patterngeneration process.

Exemplary Methods of Performing Delay Calculations

To calculate the delays at each gate in the design accurately,waveform-based simulation can be used to track the signal changes intime. Integrating the waveform simulation into the test generation tool,however, can slow down the test generation process.

In embodiments of the disclosed technology, the waveform is notsimulated explicitly. Instead, the transition arrival time and the faulteffect propagation time are used to approximate the path delay through afault site. As used in this discussion, the transition arrival time fora gate terminal z (AT_(z)) refers to the time to launch a transition atz from primary inputs or pseudo primary inputs through combinationallogic gates. The fault effect propagation time from z (PTO refers to thetime to propagate the fault effect at z to a primary output or pseudoprimary output through combinational logic gates. The path delay throughz (PD_(z)) refers to the sum of AT_(z) and PT_(z). The slack at z(S_(z)) refers to the difference between the clock period and PD_(z).

Exemplary formulas that can be used to determine the transition arrivaltime from gate inputs to its output z are given below. These formulas donot account for the delay introduced by static hazards, but can bemodified to do so if desired.

When the transition at z changes from a controlled value to anon-controlled value:

$\begin{matrix}{{{AT}_{z} = {\underset{i \in I_{cn}}{MAX}\left( {{AT}_{i} + d_{i}} \right)}},} & (1)\end{matrix}$where I_(cn) is the set of gate inputs with the value that transitionsfrom a controlling value to a non-controlling value, and d_(i) is thegate delay that propagates the transition from the ith gate input to z.Otherwise:

$\begin{matrix}{{{AT}_{z} = {\underset{i \in I_{t}}{MIN}\left( {{AT}_{i} + d_{i}} \right)}},} & (2)\end{matrix}$where I_(t) is the set of gate inputs with the transition that impliesthe transition at z; and d_(i) is the gate delay that propagates thetransition from the ith gate input to z. In one exemplary embodiment,the values of AT_(i) and d_(i) are computed from the timing informationstored in an SDF file (e.g., produced by a static timing analysis tool).

Unlike conventional path delay computation techniques, which use eitherrobust or nonrobust conditions to evaluate the propagation time startingfrom a gate terminal through a path, an exemplary embodiment of thedisclosed technology considers sensitization conditions used topropagate faults when determining the propagation time starting from afault site. This exemplary method allows reconvergent sensitizationpaths to be taken into account.

FIG. 2 is a schematic block diagram 200 illustrating a transitionpropagating through two reconvergent sensitization paths. In FIG. 2, aslow-to-fall transition fault 210 is shown on path b. Furthermore, a1-to-0 transition 220 for activating the fault (illustrated as a fallingedge, but representing the test-pattern transition 1-to-0) is shown asbeing applied to the path b as part of a test pattern. Othertest-pattern-value sequences 230, 232 are shown being applied in FIG. 2but are represented by their actual values (in FIG. 2, the first numberin the sequence represents the value applied during a first time frame,whereas the second number represents the value applied during a secondtime frame).

In FIG. 2, neither a robust test nor a nonrobust test exists to test thepath delay fault b-d-z (b-e-z) slow-to-fall. Instead, the transition atz is implied from b through reconvergent sensitization paths b-d-z andb-e-z, which both propagate the transition to a common gate 240. Whencalculating the propagation time from z to b, and according to oneexemplary embodiment, the reconvergent sensitization paths between b andz are enumerated and the propagation time at b is determined as below:

$\begin{matrix}{{{PT}_{b} = {\underset{s \in S_{rs}}{MIN}\left( {{PT}_{z} + D_{s}} \right)}},} & (3)\end{matrix}$where S_(rs) is the set of reconvergent sensitization paths, includingb-d-z and b-e-z; and D_(s) is the delay of the paths in S_(rs).

The propagation time from the sensitized input i of a gate to its outputz can be calculated as follows:PT _(i) =PT _(z) +d _(i) ^(v),  (4)where d_(i) is the gate delay to propagate the transition v at the inputi through the gate and v is a rising (or falling) transition when thefinal value at i is logic 1 (or 0). When the gate output is a stem, thepropagation time at the gate output is typically determined by themaximum propagation time among all of its branches.

Industrial designs sometimes contain combinational loops. Whencalculating arrival times and propagation times for a design withcombinational loops, and according to one exemplary embodiment of thedisclosed technology, one or more of the following criteria (alone or incombination with one another) can be used to avoid divergence during thedelay calculation: (1) to calculate the arrival time at the gate z,paths (e.g., every path) from primary inputs and/or pseudo primaryinputs to z cannot contain the same gate more than once; (2) tocalculate the propagation time at the gate z, paths (e.g., every path)from z to primary outputs and/or pseudo primary outputs cannot containthe same gate more than once; and (3) the path delay at the gate in aloop is not equal to the sum of the arrival time and the propagationtime; instead, the path delay at the gate in the loop is the delay ofthe longest path through the gate in which the path does not contain thesame gate more than once.

Exemplary Delay Test Quality Metrics

One desirable way to evaluate the quality of a test set in detectingdelay defects is to check the percentage of functional paths covered bythe test set. However, this method can sometimes be impractical due tothe exponential number of paths in the designs. According to certainembodiments of the disclosed technology, the delay defect coverage isderived from evaluating the path delays through detected transitionfaults. For example, two test quality metrics, Delay Test Coverage (DTC)and SDQM, can be determined from derived path delays. For a transitionfault f, both metrics use two types of path delay data through the faultsite.

Static path delay (PD_(f) ^(s)) refers to the longest path delay passingthrough f Static path delay can be calculated, for example, throughstructural analysis of the combinational part of the design as anapproximation for the longest functional path through f.

Actual path delay (PD_(f) ^(a)) refers to the delay that is associatedwith a test pattern t_(i) that detects f. According to one exemplarynonlimiting embodiment, the actual path delay can be defined as:

$\begin{matrix}{{{{PD}_{f}^{a}\left( t_{i} \right)} = {{AT}_{f} + {\underset{p \in P_{S}}{MAX}\left( {PT}_{f}^{p} \right)}}},} & (5)\end{matrix}$where P_(s) is all of the sensitization paths starting from f. For atest set T, and according to one exemplary nonlimiting embodiment, theactual path delay can be defined as:

$\begin{matrix}{{{PD}_{f}^{a} = {\underset{t_{i} \in T_{D}}{MAX}\left( {{PD}_{f}^{a}\left( t_{i} \right)} \right)}},} & (6)\end{matrix}$where T_(D) is the set of test patterns in T that detect f. When T_(D)is empty, PD_(f) ^(a) is equal to zero.

The Delay Test Coverage Metric

The delay test coverage (DTC) metric can be used to evaluate theeffectiveness of a test set at detecting transition faults through thelongest paths. DTC is ordinarily independent of clock frequencies andthe process-specific delay defect distribution. According to oneexemplary nonlimiting embodiment, the DTC can be defined as follows:

$\begin{matrix}{W_{f} = \frac{{PD}_{f}^{a}}{{PD}_{f}^{s}}} & (7) \\{and} & \; \\{{{DTC} = \frac{\sum\limits_{f \in F}^{\;}W_{f}}{N}},} & (8)\end{matrix}$where F is the set of transition faults and N is number of faults in F.

The upper bound of the delay test coverage is the transition fault testcoverage. In general, the closer the delay test coverage is to thetransition fault test coverage, the better the test set is at detectingtransition faults through the longest paths.

The SDQM Metric

To evaluate the quality of a test set in detecting delay defects, theSDQM typically assumes that the delay defect distribution function F(s)has been derived from the fabrication process, where s is the defectsize (incremental delay caused by the defect). Based on the simulationresults of a test set, and according to one exemplary nonlimitingembodiment, the smallest detectable delay defect size for a fault f canbe calculated as follows:

$\begin{matrix}{T_{f}^{\det} = \left\{ {\begin{matrix}{T_{TC} - {PD}_{f}^{a}} & {{{if}\mspace{14mu}{PD}_{f}^{a}} > 0} \\\infty & {{{if}\mspace{14mu}{PD}_{f}^{a}} = 0}\end{matrix},} \right.} & (9)\end{matrix}$where T_(TC) is the test clock period. The delay test quality metric,termed the “statistical delay quality level” (SDQL), can be calculatedaccording to one exemplary nonlimiting embodiment by multiplying thedistribution probability for each defect as shown below:

$\begin{matrix}{T_{f}^{mgn} = {T_{SC} - {PD}_{f}^{s}}} & (10) \\{and} & \; \\{{{SDQL} = {\sum\limits_{f \in F}^{\;}{\int_{T_{f}^{mgn}}^{T_{f}^{\det}}{{F(s)}{ds}}}}},} & (11)\end{matrix}$where T_(SC) is the system clock period and F is the fault set. Themotivation of the SDQL is to evaluate the test quality based on thedelay defect test escapes shown, for example, in the shadowed area inFIG. 3. In general, the smaller the SDQL is, the better the test qualityachieved by the test set is since the faults are detected with smalleractual slack.

Additional aspects of the SDQM are described in Y. Sato, S. Hamada, T.Maeda, A. Takatori, and S. Kajihara, “Evaluation of the StatisticalDelay Quality Model,” Proc. ASP-DAC 2005, pp. 305-310, and Y. Sato, S.Hamada, T. Maeda, A. Takatori, and S. Kajihara, “Invisible DelayQuality—SDQM Model Lights Up What Could Not Be Seen,” Proc. ITC 2005,pp. 1202-1210.

Exemplary Test Generation Embodiments Using Timing Information

To generate test sets that detect the transition faults through thelongest paths (or other desirably long paths), exemplary embodiments ofthe disclosed technology use timing information of the design to guidethe transition fault test generation process. In particular embodiments,the timing information is obtained from an SDF file (e.g., generatedfrom a static timing analysis tool) or other equivalent file and used tocompute arrival times and propagation times as discussed above. Thedisclosed test generation procedures that use timing information aregenerally referred to herein as “timing-aware ATPG.”

FIG. 4 is a flow chart showing an exemplary test generation method 400for a targeted transition fault (e.g., a transition fault selected froma list of targeted faults). The method acts shown in FIG. 4 can beperformed alone or in various combinations and subcombinations with oneanother.

At 410, a target fault is selected. For example, the target fault can beselected sequentially from a list of target faults.

At 412, the path for propagating the fault effect is determined. Duringthis method act, for example, the activated transition fault effect ispropagated to a primary output or a pseudo primary output through acircuit path. The circuit path can be the longest path, or as explainedbelow, can be selected through a weighted random selection method thatfavors the longest path, but allows other paths to be selected. Incertain implementations, if the state element driven by the pseudoprimary output is not an observation point, the fault effect is furtherpropagated through the state element until an observation point isreached. In some implementations, the delay of the propagation pathduring this second phase is disregarded.

At 414, the target fault is justified. During this method act, forexample, one or more unjustified gates used for fault activation arejustified. Furthermore, any unjustified gates used for fault propagationare justified. When the unjustified gates are used to control theactivation conditions at the fault site, they can be justified usingchoices that achieve a desirable transition arrival time at the faultsite. For example, according to one embodiment, the fault can bejustified using choices that maximize the transition arrival time at thefault site. In other desirable embodiments, and as more fully explainedbelow, the justification choices can be made according to a weightedrandom selection procedure.

At 416, the resulting test pattern portion that detects the target faultby activating the fault through the selected activation path andpropagating the fault from the fault site on the selected propagationpath is stored. For example, the test pattern portion (sometimesreferred to as a test cube) can be stored on one or morecomputer-readable media (e.g., any suitable persistent or non-persistentcomputer-readable memory). It should be understood that although themethod 400 is described as being performed for a single target fault,multiple target faults can be considered simultaneously. Any descriptionherein or in the claims of performing the described methods for a singlefault should therefore be construed to include such embodiments.

To help guide fault effect propagation and gate justification, apre-processing procedure that generates timing information can beperformed. For example, the static propagation times and the staticarrival times can be computed before test generation. For example, inone particular embodiment, the longest static propagation times and thelongest static arrival times are computed for one or more gates in thedesign (e.g., for each gate in the design). In particular embodiments,the longest static propagation times and longest static arrival timesare computed from the delay information generated by a static timinganalyzer and stored in an SDF file.

As noted above, when propagating the fault effect at a stem gatefurther, the branch with the longest static propagation delay can bepreferred in order to maximize the fault propagation time. Similarly,when justifying the gates controlling the fault activation conditions,the choice with longest static arrival time can be preferred to helpmaximize the transition arrival time to the fault site.

Accurately identifying the unjustified gate necessary to launch thetransition at the fault site can also increase the test generationcomplexity. To reduce this complexity, and according to one exemplaryembodiment, if an unjustified gate is in the combinational conedominated by the fault site, its value can be treated as a necessaryvalue to create the transition at the fault site.

Although using the longest static propagation time at the stem usuallycreates the longest sensitization path, it may potentially propagatefault effects through the same fault propagation paths repeatedly whiletargeting different faults. Besides testing the faults through thelongest paths, covering a wide range of paths is another desirablecomponent of timing-aware test generation. Testing a wide range of pathscan be desirable, for instance, because timing information is not alwaysaccurate and may not exactly reflect the actual delays experienced alonga circuit path. For example, in some cases, paths with the longest delayas computed with information from an SDF file may not in fact be thepath with the longest delay.

To achieve the testing of a wider range of paths, a weighted randommethod can be used in certain embodiments of the disclosed technology toselect the branches for fault propagation. For example, assuming thatthe fault effect is going to be propagated from a stem with n branches,the probability of selecting the branch i for fault propagation can bedetermined as follows:

$\begin{matrix}{{w_{i} = \frac{{PT}_{i}^{s}}{\sum\limits_{i = 1}^{n}{PT}_{i}^{s}}},} & (12)\end{matrix}$where PT_(i) ^(s) is the longest static propagation time from the branchi. The weighted random method assigns higher probabilities of beingselected to the paths with longer delays, but does not ignore the pathswith shorter delays.

Similar to the fault propagation, the weighted random method can also beused to select the choices to justify the gates controlling the launchconditions at the fault site. The probability of selecting ajustification choice is given below:

$\begin{matrix}{{w_{i} = \frac{{AT}_{i}^{s}}{\sum\limits_{i = 1}^{n}{AT}_{i}^{s}}},} & (13)\end{matrix}$where AT_(i) ^(s) is the longest static arrival time to the ith choiceto justify the gate and n is number of choices to justify the gate.

FIG. 5 is a flowchart 500 of a method for selecting a propagation pathusing a weighted random method. The method acts shown in FIG. 5 can beperformed alone or in various combinations and subcombinations with oneanother. At 510, the possible propagation paths are identified. At 512,weights for each of the identified paths can be computed using timinginformation. For instance, as in expression (12), the longest staticpropagation time for each of the identified paths can be used at leastin part in the weighting computation. At 514, one of the identifiedpaths is randomly selected using a procedure whereby the probability ofselecting a respective path is proportional to or otherwise based on thecomputed weight for the path.

FIG. 6 is a schematic block diagram showing an exemplary circuit portion600 illustrating how fault propagation can proceed according to a randomweighted procedure, such as by using expression (12). FIG. 6 shows agate 610 having a fault site 620 at its output where the target faulteffect occurs (here, a slow-to-rise transition fault potentially caused,for example, by some circuit defect). The fault effect can potentiallybe propagated along branches 630 (branch a), 632 (branch b), 634 (branchc) to a primary output or pseudo-primary output (not shown). Assume inthis example that a timing analysis (e.g., a static timing analysisperformed in a pre-processing step) determines that the longest staticpropagation times along the paths (PT_(x)) are as follows:

-   -   PT_(a)=10 ns    -   PT_(b)=6 ns    -   PT_(c)=2 ns        Applying expression (12), the following weights can be        determined for each choice:

$w_{a} = {\frac{10}{10 + 6 + 2} = 0.56}$$w_{b} = {\frac{6}{10 + 6 + 2} = 0.33}$$w_{c} = {\frac{2}{10 + 6 + 2} = 0.11}$One of the branches 630, 632, 634 can then be randomly selected with itsprobability of selection being determined by the computed weights.

FIG. 7 is a flowchart 700 of a method for selecting activationconditions for activating the target fault using a weighted randommethod. At 710, the possible justification choices (or fault activationconditions) for the target fault are identified. For example, possiblepaths for propagating controlling values that activate the targetedfault are identified. At 712, weights for each of the identifiedjustification choices can be computed using timing information. Forinstance, as in expression (13), the longest static arrival time foreach choice can be used at least in part in the weighting computation.At 714, one of the identified choices is randomly selected using aprocedure whereby the probability of selecting a respective choice isproportional to or otherwise based on the computed weight for thechoice.

FIG. 8 is a schematic block diagram showing an exemplary circuit portion800 illustrating how fault activation can proceed according to a randomweighted procedure, such as by using expression (13). FIG. 8 shows afirst gate 810 with three inputs 830 (input a), 832 (input b), and 834(input c). FIG. 8 further shows a fault site 820 at the output of thegate 810 where the target fault is desirably activated and an exemplarypropagation path 840 to a primary output 842 (here, a scan cell). Thefault can potentially be activated at the output of the first gate 810by justifying controlling values to one of the inputs 830, 832, 834 ofthe first gate 810. Assume in this example that a timing analysis (e.g.,a static timing analysis performed in a pre-processing step) determinesthat the longest static arrival times (AT_(x)) of values at each of theinputs a, b, and c are as follows:

-   -   AT_(a)=8 ns    -   AT_(b)=3 ns    -   AT_(c)=2 ns        Applying expression (13), the following weights can be        determined for each choice:

$w_{a} = {\frac{8}{8 + 3 + 2} = 0.62}$$w_{b} = {\frac{3}{8 + 3 + 2} = 0.23}$$w_{c} = {\frac{2}{8 + 3 + 2} = 0.15}$One of the inputs 830, 832, 834 can then be randomly selected with itsprobability of selection being determined by the computed weights.

Fault Simulation

To derive the delay test quality of a test set, the fault simulationprocess is desirably enhanced to utilize the actual path delays for eachdetected fault. For example, a transition-based method and/or apath-based method can be used to calculate the actual path delays.

In certain exemplary embodiments of the disclosed technology that use atransition-based method, a detected fault f is not dropped from thefault list during fault simulation unless the difference between thestatic path delay and the actual path delay off is not greater than thedifference between test clock period and system clock period. Since theevaluation of static path delay is typically not accurate and isgenerally greater than the delay of the longest functionallysensitizable path, this method can result in high computationalcomplexity. However, these embodiments can provide an exact way toidentify the sensitization paths to propagate the fault effects.

Path-based methods can generally be viewed as non-fault-orientedmethods. According to certain exemplary embodiments of the disclosedtechnology that use path-based methods, actual path delays are derivedfrom good machine simulations of test patterns (e.g., of each testpattern in a test set). In comparison to transition-based methods,embodiments of the path-based method typically have smaller faultsimulation times.

In particular implementations using a path-based method, non-robustconditions or robust conditions are used as sensitization conditions totrace the circuit backward (e.g., from each observation point), in orderto identify the faults detected at the observation points. However, suchpath-based methods typically cannot identify all of the detectedtransition faults since faults detected through reconvergentsensitization paths generally cannot be found with non-robustconditions. Thus, in particularly desirably embodiments, relaxed pathtracing conditions (instead of robust or nonrobust conditions) are usedto guide the backward tracing. In general, a sensitization conditionalso exists when there are multiple controlling transitions at theinputs of a gate on possible fault propagation paths. A controllingtransition is a transition that stabilizes at the controlling value of agate input (e.g., a 1 to 0 transition for AND and NAND gates and a 0 to1 transition for OR and NOR gates). In FIG. 2, for example, the risingtransitions on paths d and e at the inputs of the OR gate 240 are bothcontrolling transitions as they stabilize to 1. Furthermore, if themultiple controlling transitions at the gate can be traced to a commonsource (a reconvergent source) that is affected by the targeted fault,then the fault is detectable on the fault propagation path. Thus, byconsidering sensitization conditions, reconvergent sensitization pathscan be identified during the backward tracing procedure and detectedtransition faults that would not be identified when requiring robust ornonrobust condition can be identified. Unless otherwise stated, thepath-based method using sensitization conditions and described above wasused in the experiments described below for calculating the actual pathdelays.

FIG. 9 is a flowchart showing an exemplary method 900 for performingfault simulation. The method acts shown in FIG. 9 can be performed aloneor in various combinations and subcombinations with one another.Furthermore, the particular sequence shown should not be construed aslimiting (e.g., method acts 912 and 914 can be performed in a differentorder).

At 910, good machine simulation is performed for test pattern t_(i). Forexample, a simulation (e.g., a logic simulation) of the integratedcircuit design can be performed to determine how the gates of thecircuit design respond to the test values of the test pattern t_(i).

At 912, fault simulation is performed for undetected faults of a targetfault list. For example, the circuit design's response to the testpattern t_(i) in the presence of the undetected faults can be simulated.In particular embodiments, each undetected fault from the fault list isfault simulated. In certain embodiments, if the undetected faults thatare simulated are detected by the test pattern t_(i), they are removedfrom the fault list. However, in embodiments discussed in more detailbelow, one or more fault dropping criteria are used to determine whetherthe fault is to be removed from the fault list. When fault droppingcriteria are used, the determination of whether to remove the fault fromthe fault list may not occur until the necessary timing information isdetermined (e.g., until after method act 922 has been performed for aselected fault).

At 914, backward tracing is performed from one or more observationpoints of the integrated circuit design to identify sensitization paths.In particular embodiments, backward tracing is performed using the goodmachine simulation results and from each observation point (e.g., eachprimary output and pseudo primary output). Furthermore, in certainembodiments, the maximum propagation times are determined for one ormore gates in the sensitization paths (e.g., for each gate in thesensitization path).

At 916, a detected fault f from the original fault list is selected. Thedetected fault selected can be a fault detected by an earlier testpattern and/or one of the faults determined at 912 to be detected by thetest pattern t_(i).

At 918, a determination is made as to whether the selected fault f is inone of the identified sensitization paths and whether the activationcondition for f is met. If the selected fault f is in one of theidentified sensitization paths and if its activation condition is met,the method 900 continues at 920; otherwise, the method proceeds to 926where a determination is made as to whether there are any additionaldetected faults to consider, and if so the next detected fault f fromthe original list is selected at 916.

At 920, the arrival time to the fault f is determined. For example, themaximum arrival time to the fault f is determined.

At 922, the actual path delay passing through f is determined. Forexample, the actual path delay is determined by combining the maximumpropagation time determined at 914 and the maximum arrival timedetermined at 920.

At 924, the maximum actual path delay through f is updated if thecurrent actual delay is larger. That is, in certain embodiments, eachfault has associated with it a maximum actual path delay that is storedwith the fault. The actual path delay can be used for example to derivethe test quality or to help guide the fault dropping process. If thecurrent actual delay computed at 924 is larger than the previouslystored maximum actual path delay, the path delay is updated.

At 926, a determination is made as to whether any additional detectedfaults remain to be considered. If so, then the method 900 return to 916and the next detected fault is selected; otherwise, the method 900 ends.

Although arrival times are shown as being determined on a per-faultbasis in the above method acts, they can be determined simultaneouslywith one or more other faults. For example, the arrival times for allfaults can be determined simultaneously.

FIG. 10 is a schematic block diagram of an exemplary circuit portion1000 illustrating aspects of the method 900. For example, circuitportion 1000 has three observation points 1010, 1012, 1014. In theexample shown in FIG. 10, observation points 1010, 1012 are scan cellinputs (and thus comprise pseudo primary outputs), whereas theobservation point 1014 is an output pin (and thus comprises a primaryoutput). Sensitized paths 1020, 1022, 1024 from each of the observationpoints 1010, 1012, 1014 are also illustrated. The sensitization paths1020, 1022, 1024 are illustrated schematically as logic cones, though itshould be understand that they represent the paths whose value at therespective primary output is controllable by changing the value at asingle input (e.g., a scan cell or input pin). As noted above withrespect to FIG. 9, the sensitization paths are determined using goodsimulation results for a particular test pattern t_(i) at 914. FIG. 10also illustrates an exemplary fault 1030 selected from the fault list.In this example, fault 1030 is in one of the sensitized paths 1022.Therefore, according to the method 900, the actual path delay for thefault is determined by computing the maximal arrival time for thesensitized path that activates and propagates the fault 1030 to thepseudo primary output 1012 (illustrated as path 1032). If the actualpath delay computed is greater than the previously stored actual pathdelay, then the actual path delay for the fault is updated by storingthe new actual path delay.

Fault Dropping Criteria

After a test pattern or a subset of test patterns is generated,conventional test generators fault simulate all of the undetected faultsin order to find the faults detected by chance and remove them from thetarget fault list. This strategy can help reduce the test generationtime. However, using detection as the only criterion to drop a faultdoes not mean that the delay faults will be detected through the longest(or other desirably long) paths since the path detecting the fault maynot be the longest sensitizable path (or other desirably long path)through that fault site. In general, the longest sensitizable paths (orother desirably long paths) to detect a delay defect are unknown inadvance, and the structure-based static path analysis only provides anupper bound for the longest delays passing through gates.

In certain embodiments, a deterministic test generator can be used toidentify the longest sensitizable paths through fault sites such that adetected fault cannot be dropped from the fault list unless it istargeted by the deterministic test generator explicitly or the actualdelay through the fault site is equal to the longest static delay.However, using this fault dropping criterion can increase the testgeneration effort and may be impractical to apply on large industrialdesigns.

In certain other embodiments, multiple detection can be used as anadditional fault dropping condition in order to improve the possibilityof detecting faults through the longest (or other desirably long) paths.However, the experimental results given below show that the increase ofdetection times has limited improvement on the delay test coverage.

In certain desirable embodiments of the disclosed technology, a faultdropping criterion based at least in part on the actual path delay isused. For example, a criterion, named “Dropping Based on Slack Margin”(DSM) can be used. DSM allows a tradeoff among the test generationeffort, test pattern count, and the test set quality for delay detects.

According to one exemplary embodiment of the DSM technique, a fault f isdropped from the target fault list if a test pattern t_(i) detects f andthe actual path delay created by t_(i) satisfies the followingcondition:

$\begin{matrix}{\frac{{PD}_{f}^{s} - {PD}_{f}^{a}}{T_{TC} - {PD}_{f}^{a}} < \delta} & (14)\end{matrix}$where T_(TC) is test clock period and δ is a real number between 0 and 1and may be selected by the user. Expression (14) means that a fault isdropped when the relative difference between the actual slack and thestatic slack of a path (the slack margin) is less than some predefinedlimit. Other criteria based at least in part on the actual path delaycan also be used. (Note that the mathematical operation in expression(14) and the other expressions in this disclosure may vary fromimplementation to implementation (e.g., the operations may be ≤, >, ≥),depending, for example, on whether the criterion is used to determinewhether a fault should be dropped or used to determine whether a faultshould be left remaining on the list.)

The criterion DSM with 1=δ is equivalent to the traditional faultdropping criterion. Further, when 0=δ, every fault will be targeted bythe deterministic test generator. In general, as smaller values of S arechosen for test generation, the test pattern counts increase.

FIG. 11 is a flowchart of an exemplary embodiment 1100 for applying thefault dropping criterion. At 1110, fault simulation is performed for atest pattern to determine the actual path delays. For example, the faultsimulation procedure 900 illustrated in FIG. 9 can be performed for atest pattern t_(i). At 1112, a fault detected by the test pattern t_(i)is selected. For example, one of the faults that was determined to bedetected by the test pattern t_(i) (e.g., at 912) can be selected. At1114, a determination is made as to whether the fault should be removedfrom the fault list based at least in part on the actual slack of thepath. For example, a criteria based on the slack margin (such as thecriteria in expression (14)) can be used. Based on the outcome of thedetermination at 1114, the fault is either removed at 1116 or leftremaining on the fault list. At 1118, a determination is made as towhether any faults remain on the fault list that were detected by thetest pattern t_(i). If so, the method returns to 1112 and the next faultis selected; otherwise, the method 1100 terminates.

Although the method 1100 is shown as being separate from the faultsimulation method 900 in FIG. 11, portions of the procedure can beintegrated into the fault simulation procedure. For example, method acts1114, 1116 can be performed during the fault simulation method 900(e.g., after the actual path delay for each detected fault isdetermined).

Test Quality Evaluation for Industrial Designs

Two industrial designs were used to evaluate the test set qualitygenerated by embodiments of the timing-aware ATPG technique. Thecharacteristics of the designs are shown in Table 1. The nominal delaysdefined in SDF files were used to calculate the path delays. Tocalculate SDQL, the delay defect distribution was calculated accordingto the delay defect distribution function F(s) described in Y. Sato, S.Hamada, T. Maeda, A. Takatori, and S. Kajihara, “Invisible DelayQuality—SDQM Model Lights Up What Could Not Be Seen,” Proc. ITC 2005,pp. 1202-1210:F(s)=1.58×10⁻³ ×e ^(−2.1s)+4.94×10⁻⁶,  (15)

TABLE 1 Characteristics of the Designs |G| |FF| |CLK| SDQL |SDF| Case-1240K 14.6K 2 241.6 854K Case-2 2.43M 69.1K 4 783 4.4M

In Table 1, |G| is the number of gates in the design, |FF| is the numberof sequential elements, |CLK| is the number of clocks, SDQL is the SDQLlevel in parts per million (ppm) before applying any test patterns, and|SDF| is the number of delay statements defined in SDF file.

For each design, three types of experiments were performed to generatethree groups of broadside transition fault test sets. In the firstexperiments (Exp. 1), traditional ATPG was performed. During theexperiments, a random decision order was used when launching andpropagating the fault effect. A fault was dropped from the fault listonce it was detected by the fault simulator N times. In the secondexperiments (Exp. 2), timing-aware ATPG was performed without using theDSM fault-dropping criteria. In particular, integrated timinginformation from SDF was used to guide the test generation. The weightedrandom method described above and using expressions (12) and (13) wasused during test generation. A fault was dropped from the fault listonce it was detected by the fault simulator N times. In the thirdexperiments (Exp. 3), timing-aware ATPG with the DSM fault-droppingcriteria shown in expression (14) was performed. The setup was the sameas Exp. 2, but multiple detection was not used. Instead, detected faultswere dropped based on the DSM criterion introduced above to improve thetest set quality.

The test generation results for the two designs are shown in Table 2 andTable 3, respectively. For the first two experiments, the number ofdetections was run up to 20 for both designs. When applying the DSMcriterion in the third experiment, δ was set to 1, 0.5, 0.25, and 0. Foreach ATPG run, four numbers are reported in the tables to show the testgeneration results: number of generated test patterns denoted as |P|,test coverage denoted as TC, delay test coverage denoted as DTC, andSDQL in parts per million (ppm).

TABLE 2 Test generation results for Case-1 |P| TC DTC SDQL Initial 0 0 0241.6 Exp. 1 - Traditional ATPG N = 1 5,217 90.99% 84.59% 36.34 N = 36,352 91.12% 85.04% 35.37 N = 5 6,730 91.15% 85.10% 35.18 N = 7 7,09391.19% 85.18% 35.00 N = 15 8,184 91.23% 85.24% 34.38 N = 20 8,932 91.24%85.25% 34.18 Exp. 2 - Timing-Aware ATPG N = 1 5,233 90.86% 84.64% 36.45N = 3 6,438 91.03% 85.10% 35.41 N = 5 6,743 91.09% 85.21% 35.12 N = 77,120 91.13% 85.30% 34.85 N = 15 8,277 91.20% 85.39% 34.61 N = 20 8,93791.22% 85.41% 34.57 Exp. 3 - Timing-Aware ATPG with DSM Criteria δ = 15,233 90.86% 84.64% 36.45 δ = 0.5 9,851 90.95% 85.70% 34.16 δ = 0.2518,695 91.06% 86.62% 32.16 δ = 0 64,369 91.16% 87.81% 29.28

TABLE 3 Test generation results for Case-2 |P| TC DTC SDQL Initial 0 0 0783 Exp. 1 - Traditional ATPG N = 1 3,668 91.23% 66.13% 214.8 N = 35,829 91.27% 67.26% 208.9 N = 5 6,955 91.27% 67.73% 206.4 N = 7 7,97991.27% 68.07% 204.6 N = 15 12,254 91.28% 69.01% 199.5 N = 20 14,93291.28% 69.41% 197.4 Exp. 2 - Timing-Aware ATPG N = 1 3,508 91.19% 67.39%208.9 N = 3 5,430 91.24% 68.37% 203.6 N = 5 6,615 91.26% 68.79% 201.4 N= 7 7,624 91.26% 69.13% 198.6 N = 15 12,013 91.27% 70.25% 193.5 N = 2014,526 91.28% 70.73% 190.9 Exp. 3 - Timing-Aware ATPG with DSM Criteriaδ = 1 3,508 91.19% 67.39% 208.9 δ = 0.5 8,642 91.26% 76.26% 160.5 δ =0.25 13,937 91.27% 77.09% 156.2 δ = 0 24,493 91.28% 77.71% 152.9

When comparing Exp. 1 with Exp. 2 for the same value of N, it can beseen that timing-aware ATPG achieved better test quality in terms ofdelay test coverage, and a similar number of test patterns weregenerated. The delay test coverage improvement was more significant forthe design Case-2. For example, the delay test coverage increased by1.26% when N=1 and by 1.32% when N=20. After analyzing the limitedimprovement in the delay test coverage with the timing-aware ATPG forthe design Case-1, it can be observed that most paths in the design havesimilar delays and the test generation guided by timing information hasless impact on the overall test quality for the delay faults. Thisobservation can also be seen from the difference between the delay testcoverage and the test coverage. When N=1, the difference was only 6.4%for the design Case-1. However, it was 25.1% for the design Case-2.Although the delay test coverage improvement with the timing-aware ATPGwas limited for Case-2, the timing-aware ATPG generated fewer testpatterns while achieving the same level of delay test coverage. Forexample, 7,120 test patterns were generated with the timing-aware ATPGwhen N=7 and it achieved 85.30% delay test coverage. However, thetraditional ATPG required more than 8,932 test patterns to achieve asimilar level of delay test coverage. When measuring the test quality bySDQL, both the traditional ATPG and the timing-aware ATPG achieved asimilar level of SDQL for design Case-1 due to the similar delays formost of paths in the design. However, a significant improvement wasachieved for design Case-2. For example, the SDQL was reduced from 214.8to 208.9 when N=1.

The effectiveness of using SDM as a fault dropping criterion can beobserved for both designs. From Table 2 and Table 3, it can be seen thatsignificant delay test coverage and SDQL improvements were achieved as 5decreased. When comparing δ=0.5 with Exp. 2 with largest N, the delaytest coverage increased from 85.41% to 85.70% for the design Case-1, andfrom 69.13% to 76.26% for the design Case-2. The SDQL was reduced from34.57 to 34.16 for the design Case-1, and from 198.6 to 160.5 for thedesign Case-2. The test pattern count increased by 88.25% and 135.6%when comparing δ=0.5 with the traditional ATPG with N=1. However, forthe design Case-2, 42.12% less of test patterns are generated whencomparing with the traditional ATPG with N=20.

From Table 3, it can also be seen that multiple detection alone hadlimited effectiveness on improving the test quality for delay defects.The ATPG results also illustrate that multiple detection may not besuitable for achieving higher test quality for small delay defects whenthe path length in the design is unbalanced. Embodiments of thetiming-aware ATPG method, however, can be used to improve the testquality, particularly for such types of designs.

To illustrate the effectiveness of the timing-aware ATPG at detectingdelay faults through longer paths further, FIG. 12 is a graph 1200showing the distribution of the differences between the maximal staticpath delay and the maximal actual path delay through each detectedtransition fault by the traditional ATPG with N=1 for the design Case-2.It can be seen that 50% of detected faults have path delay differencesless than 0.54 ns. When the path delay difference reaches 1.43 ns, 90%of detected faults are covered. Rather than showing the distribution ofthe static and actual path delay differences for the test sets generatedby timing-aware ATPG directly, graphs 1300, 1400, 1500 of FIGS. 13, 14,and 15 show the distribution differences between the traditional ATPGwith N=1 and the timing-aware ATPG with N=1, N=20, and DSM=0.5,respectively. As seen, more detected faults move to the region withfewer differences. For the timing-aware ATPG with N=1, N=20, and DSM=0,the percentages of covered detected faults become 52.8%, 56.8%, and69.5% at 0.54 ns and become 90.3%, 93.1%, and 94.6% at 1.43 ns. Theseresults demonstrate that embodiments of the timing-aware ATPG method canimprove the test set quality and the test sets ability to detect smalldelay defects.

It should be noted that in the reported experiments, the test coverageachieved by the timing-aware ATPG was slightly lower than that achievedby the traditional ATPG. The main reason is that the exemplaryembodiments of the timing-aware ATPG method that were tested attemptedto propagate the fault effects and to justify the gates through thelongest paths. This likely caused more faults to be aborted during testgeneration when both ATPG methods had the same backtrack limit.Increasing the backtrack limit when performing embodiments of the ATPGmethod can help reduce the gap between test coverage differences.Another way to reduce the test coverage gap is to try the aborted faulta second time with traditional ATPG.

Timing Critical Faults

When a delay defect is present in a circuit, the defect's impact on thenormal operation of the circuit depends on the defect's location anddelay fault size. If the delay fault size is greater than the slack ofthe shortest functional path, S_(min), the circuit will malfunctionindependent of the delay defect's location in the functional paths. Testpatterns generated based on the traditional transition fault model canordinarily detect this type of delay defect during at-speed testing. Ifthe delay fault size is less than the slack of the longest functionalpath, S_(max) the circuit will operate correctly even if the delaydefects are presented in the functional paths. When the delay fault sizeis between S_(min) and S_(max), the circuit will malfunction duringnormal operation if the sum of the longest path delay passing throughthe defect and extra delay introduced by the defect is greater than thesystem clock period; otherwise, the circuit will still operatecorrectly.

In certain embodiments, a timing-aware deterministic test generator isused to test transition faults (e.g., every transition fault) throughthe longest sensitizable path. Furthermore, in certain implementations,a fault is not dropped from the fault list unless it is targeted by thedeterministic test generator explicitly or unless a slack margin (DSM)criterion is met. In some cases, however, this methodology produces anundesirably high test pattern count.

To address this issue, certain desirable embodiments of the disclosedtechnology target a subset of transition faults explicitly by using atiming-aware deterministic test generation procedure (e.g., any of theabove-described test pattern generation procedures that use timinginformation) whereas the remainder of the transition faults are targetedby a deterministic test generation procedure that does not take timinginformation into consideration. This procedure allows a tradeoff amongthe test generation effort, test pattern count, and test set quality fordelay defect. This procedure also takes into account the fact that smalldelay defects have a higher probability of being introduced duringfabrication than large delay defects. Functional paths with tight slackmargins are more vulnerable to violate timing constraints in thepresence of the small delay defects.

According to one exemplary embodiment, a fault f is classified as aso-called “timing critical fault” that is desirably targeted by atiming-aware deterministic test generation procedure if the static pathdelay associated with f satisfies the following condition:

$\begin{matrix}{{\frac{T_{TC} - {PD}_{f}^{s}}{T_{TC}} < \lambda},} & (16)\end{matrix}$where T_(TC) is the test clock period and k is a real number between 0and 1 and may be selected by the user. Expression (16) means that afault is in a timing critical functional path when the minimum slackmargin is less than some predefined limit. Other criteria based at leastin part on the static path delay can also be used.

In the described example, when the critical fault identificationcriterion is 1 (λ=1), all transition faults are classified as timingcritical faults. In general, as smaller values of λ are chosen for testgeneration, fewer transition faults are classified as timing criticalfaults and thus the test pattern counts generated by the timing-awaredeterministic test generation procedure decrease.

FIG. 16 is a flowchart of an exemplary embodiment 1600 for performingtest pattern generation using the existence of timing critical faults asan additional criterion. At 1610, the target fault list is generated. At1612, timing critical faults are identified from the target fault list.For example, in one desirable embodiment, timing critical faults areidentified using the criterion shown in expression (16). At 1614, afault from the target fault list is selected (e.g., the next fault) andis targeted at 1616 by the timing-aware deterministic test generationprocedure. For instance, the test generation procedure 400 illustratedin FIG. 4 can be performed to generate a test pattern t_(i) detectingthe target fault. To simplify the test generation process and improvethe chance of detecting the non-timing-critical faults, the timing-awaredeterministic test generation procedure can be used for all explicitlytarget faults in this exemplary embodiment. At 1618, fault simulation iscarried out to identify the faults detected by t₁. In the illustratedembodiment, if a non-timing-critical fault is detected, it is droppedfrom the target fault list. If a timing-critical-fault is detected, itis dropped from the target fault list if it has been targeted explicitlyby the deterministic test generation procedure or if it meets the faultdropping criterion based on actual delay (e.g., the DSM fault droppingcriterion described above). At 1620, a determination is made as towhether there are any more faults in the target fault list. If so, themethod returns to 1614 and the next target fault is selected from thetarget fault, list; otherwise, the method 1600 terminates.

In other exemplary embodiments, the target fault list only includestiming critical faults and the non-timing critical faults are ignoredduring timing-aware deterministic test pattern generation. This strategyallows additional tradeoff among the test generation effort, testpattern count, and the test set quality for delay defects.

Test Generation Results for Timing Critical Faults

Four industrial designs were used to evaluate test generation resultsfrom the test pattern generation method described above that uses timingcritical faults as an additional criterion. FIG. 17 is a graph 1700showing the distributions of the timing critical faults for fourindustry designs. It can be seen that the number of timing criticaltransition faults decreases as λ decreases. For the same λ, the numberof timing critical transition faults is circuit dependent. When λ=0.25,fewer than 10% of transition faults are timing critical in ckt1 andckt2, but more than 25% of transition faults are timing critical in ckt3and ckt4.

For each design shown in FIG. 17, three types of experiments wereperformed to generate broadside transition fault test sets. In the firstexperiment (Exp. 1), traditional ATPG was performed. In particular, afault was dropped from the fault list once it was detected by the faultsimulator. In the second experiment (Exp. 2), timing-aware ATPG with theDSM fault-dropping criterion shown in expression (14) was performed andδ was set to 0.5. In the third experiments (Exp. 3), timing-aware ATPGfor the timing critical faults identified based on the criterion shownin expression (16) was performed and λ was set to 0.25, 0.2, 0.15, and0.1, respectively. Meanwhile, the DSM criterion with δ=0.5 was used asan additional fault dropping criterion for the timing critical faults.For all the experiments, the delay test coverage (DTC) shown inexpression (8) was used to measure the delay test quality.

The test generation results for the four industrial designs are shown inTable 4. After the design name, the transition fault test coverage isindicated in the column “TC.” The test generation results for Exp. 1 andExp. 2 are shown under the columns “Trad.” and “DSM δ=0.5”,respectively. Under the columns “λ=0.25,” “λ=0.2,” “λ=0.15,” and“λ=0.1,” the test generation results for Exp. 3 are shown. The testpattern count and delay test coverage for each experiment are shownunder the sub-columns “Pat.” and “DTC,” respectively. It can be seenthat the timing-aware ATPG with DSM δ=0.5 generated 46.85% to 139.57%more test patterns than the traditional transition fault ATPG. However,the delay test coverage was improved by 1.8% to 7.46%. By usingtiming-aware ATPG to target timing critical faults only, the number ofgenerated test patterns was reduced compared to when the DSM alone wasused (δ=0.5). In ckt2 and ckt3, the test pattern count with λ=0.1 isclose to the test pattern count from using traditional ATPG. Althoughthe delay test coverage dropped by 0.87% and 2.12% when comparing withDSM δ=0.5. 1.41% and 5.34% delay test coverage improvements are achievedwhen comparing the results with traditional transition fault ATPG. Inckt1 and ckt4, the test pattern count reduction is not sensitive to λsince the percentage of timing critical transition faults does notreduce much as λ decreases. However, the test pattern count with λ=0.1is still 8.9% less than the test pattern count with DSM alone and thedelay test coverage decreases by only 0.07% and 0.19%, respectively. Theexperimental results shown in Table 4 demonstrate that targeting thetiming critical transition faults by the timing-aware ATPG helps toreduce the test pattern count while having a moderate impact on theoverall delay test coverage.

TABLE 4 Test generation results for timing critical faults Trad. DSM δ =0.5 λ = 0.25 λ = 0.2 λ = 0.15 λ = 0.1 Ckt TC Pat. DTC Pat. DTC Pat. DTCPat. DTC Pat. DTC Pat. DTC ckt1 94.66 2847 88.02 4181 89.82 3966 89.723918 89.71 3849 89.74 3809 89.75 ckt2 89.96 19424 72.72 30858 75.0027479 74.61 26067 74.52 23021 74.62 21282 74.13 ckt3 90.05 3882 67.996073 75.45 5719 75.04 5484 74.62 4885 73.66 3932 73.33 ckt4 91.38 3304878.36 79172 81.23 75838 81.17 73986 81.08 74846 81.10 72125 81.04Detecting Holding Time Violations

Another class of defects that can be addressed using embodiments of thedisclosed technology are defects that cause holding time violations (orhold time violations). In general, if the data hold time at a stateelement's data input violates the design specification, a circuit maymalfunction. To detect hold-time-related defects, the timing-aware ATPGprocedure is desirably modified so that instead of creatingsensitization paths with longer delays, the ATPG procedure createssensitization paths with shorter delays (e.g., the shortest delay).Exemplary modifications to the above-described timing-aware ATPGtechniques that can be performed to accomplish this objective aredescribed in the sections below.

Exemplary Methods of Performing Delay Calculations for Holding TimeViolations

For hold time violations, the calculation for the arrival time at a gateis the same as expressions (1) and (2). To distinguish from expressions(1) and (2), the variables denoting the arrival time are changed fromAT_(z) and AT_(i) to HAT_(z) and HAT_(i), respectively. Thus,expressions (1) and (2) can be rewritten as follows:

$\begin{matrix}{{{HAT}_{z} = {\underset{i \in I_{CN}}{MAX}\left( {{HAT}_{i} + d_{i}} \right)}},} & (17) \\{{{HAT}_{z} = {\underset{i \in I_{t}}{MIN}\left( {{HAT}_{i} + d_{i}} \right)}},} & (18)\end{matrix}$

The calculation for the propagation time through reconvergentsensitization paths is the same as expressions (3). To distinguish fromexpression (3), the variables denoting the propagation time inexpression (3) are changed from PT_(b) and PT_(z) to HPT_(b) andHPT_(z), respectively, for holding time violations. Thus, the expressioncan be rewritten as follows:

$\begin{matrix}{{{HPT}_{b} = {\underset{s \in S_{rs}}{MIN}\left( {{HPT}_{z} + d_{s}} \right)}},} & (19)\end{matrix}$

The calculation for the propagation time from the sensitized input i ofa gate to its output z is the same as expression (4). To distinguishfrom expression (4), the variables denoting the propagation time inexpression (4) are changed from PT_(i) and PT_(z) to HPT_(i) andHPT_(z), respectively, for holding time violations. Thus, the expressioncan be rewritten as follows:HPT _(i) =HPT _(z) +d _(i) ^(v),  (20)In certain embodiments, for holding time violations, the definition ofthe static path delay is changed from referring to the longest pathdelay passing through f to the shortest path delay passing through f.The static path delay can be calculated, for example, through structuralanalysis of the combinational part of the design as an approximation ofthe shortest functional path through f. To distinguish from the longeststatic path delay PD_(f) ^(s), the shortest static path delay is denotedas HPD_(f) ^(s).

Similarly, for holding time violations, the definition for actual pathdelay is changed from referring to the longest sensitization pathdetecting f to the shortest sensitization path detecting f. Todistinguish from the longest path delay PD_(f) ^(a), the actual pathdelay is denoted as HPD_(f) ^(a). The calculation for the shortestactual path delay that detects the defects is changed accordingly. Forone exemplary embodiment, the shortest actual path delay associated witha test pattern t_(i) that detects f is defined as:

$\begin{matrix}{{{{HPD}_{f}^{a}\left( t_{i} \right)} = {{AT}_{f} + {\underset{p \in P_{S}}{MIN}\left( {HPT}_{f}^{p} \right)}}},} & (21)\end{matrix}$where P_(s) is all of the sensitization paths starting from f. For atest set T, and according to one exemplary embodiment, the shortestactual path delay can be defined as:

$\begin{matrix}{{{HPD}_{f}^{a} = {\underset{t_{i} \in T_{D}}{MIN}\left( {{HPD}_{f}^{a}\left( t_{i} \right)} \right)}},} & (22)\end{matrix}$where T_(D) is the set of test patterns in T that detect f. When T_(D)is empty, HPD_(f) ^(a) is equal to infinite.

The Holding Time Test Coverage Metric

The holding time test coverage (HTTC) metric can be used to evaluate theeffectiveness of a test set at detecting holding time faults through theshortest paths. According to one exemplary nonlimiting embodiment, theHTTC can be defined as follows:

$\begin{matrix}{W_{f} = \frac{{HPD}_{f}^{s}}{{HPD}_{f}^{a}}} & (23) \\{and} & \; \\{{{HTTC} = \frac{\sum\limits_{f \in F}^{\;}W_{f}}{N}},} & (24)\end{matrix}$where HPD_(f) ^(a) is the shortest static path delay through fault f; Fis the set of holding time faults; and N is number of faults in F.

Exemplary Timing-Aware Test Generation Embodiments for Holding TimeViolations

The test generation procedures for holding time faults are the same asthe above-described test generation procedures for delay faults exceptthat different weights used for guiding fault propagation and gatejustification are used.

For fault propagation, the weight of a branch for a stem with n branchescan be computed as follows:

$\begin{matrix}{{w_{i} = \frac{\frac{1}{{HPT}_{i}^{s}}}{\sum\limits_{i = 1}^{n}\frac{1}{{HPT}_{i}^{s}}}},} & (25)\end{matrix}$where n is the number of possible fault propagation paths, i is an indexvalue, and HPT_(i) ^(s) is the shortest static propagation time for thepossible fault propagation path i. The probability of selecting thebranch i for fault propagation is based on the weight.

For gate justification, the weight for each justification choice can becomputed as follows:

$\begin{matrix}{{w_{i} = \frac{\frac{1}{{HAT}_{i}^{s}}}{\sum\limits_{i = 1}^{n}\frac{1}{{HAT}_{i}^{s}}}},} & (26)\end{matrix}$where HAT_(i) ^(s) is the shortest static arrival time to the ith choiceto justify the gate and n is number of choices to justify the gate. Theprobability of selecting the choice i for gate justification is based onthe weight.

Fault Dropping Criteria for Holding Time Violations

Similar to the fault dropping criteria used for delay defects, two faultdropping criteria can be used for dropping the holding time faults fromthe target fault list in order to allow a tradeoff among the testgeneration effort, test pattern count, and test set quality for holdingtime defects.

The first fault dropping criterion drops a fault if the actual pathdelay detecting the fault is short enough. According to one exemplaryembodiment, a fault f is dropped from the target fault list if a testpattern t_(i) detects f and the shortest actual path delay created byt_(i) satisfies the following condition:

$\begin{matrix}{{\frac{{HPD}_{f}^{a} - {HPD}_{f}^{s}}{T_{TC} - {HPD}_{f}^{s}} < \delta},} & (27)\end{matrix}$where T_(TC) is the test clock period and δ is a real number between 0and 1 and may be selected by the user. Other criteria based at least inpart on the actual path delay can also be used.

The second fault dropping criterion drops a fault if the shortest staticpath delay associated with the fault is large enough. According to oneexemplary embodiment, a fault f is dropped from the target fault list ifa test pattern t_(i) detects f and the shortest static path delayassociated with f satisfies the following condition:

$\begin{matrix}{{\frac{T_{TC} - {HPD}_{f}^{s}}{T_{TC}} < \lambda},} & (28)\end{matrix}$where λ is a real number between 0 and 1 and may be selected by theuser. The two fault dropping criteria described above can be usedsimultaneously or separately during test pattern generation.Exemplary Distributed Computing Network Embodiments

Any of the aspects of the technology described above may be performedusing a distributed computer network. FIG. 18 shows one suitableexemplary network. A server computer 1800 can have an associated storagedevice 1802 (internal or external to the server computer). For example,the server computer 1800 can be configured to generate test patterns ortest pattern values using any of the disclosed methods (for example, aspart of an EDA software tool, such as a test pattern generation tool).The server computer 1800 can be coupled to a network, shown generally at1804, which can comprise, for example, a wide-area network, a local-areanetwork, a client-server network, the Internet, or other suitablenetwork. One or more client computers, such as those shown at 1806,1808, may be coupled to the network 1804 using a network protocol. Thework may also be performed on a single, dedicated workstation, which hasits own memory and one or more CPUs.

FIG. 19 shows another exemplary network. One or more computers 1902communicate via a network 1904 and form a computing environment 1900(for example, a distributed computing environment). Each of thecomputers 1902 in the computing environment 1900 can be used to performat least a portion of the test pattern generation process. The network1904 in the illustrated embodiment is also coupled to one or more clientcomputers 1908.

FIG. 20 shows that design information for a circuit-under-test (forexample, an HDL file, netlist, GDSII file, Oasis file, or other suitabledesign file representing the circuit-under-test together with its scanchains) can be analyzed using a remote server computer (such as theserver computer 1800 shown in FIG. 18) or a remote computing environment(such as the computing environment 1900 shown in FIG. 19) in order togenerate test patterns or test pattern values according to anyembodiment of the disclosed technology. At process block 2002, forexample, the client computer sends the integrated circuit designinformation to the remote server or computing environment. In processblock 2004, the integrated circuit design information is received andloaded by the remote server or by respective components of the remotecomputing environment. In process block 2006, test pattern generation isperformed to produce test patterns according to any of the disclosedembodiments. At process block 2008, the remote server or computingenvironment sends the resulting test patterns to the client computer,which receives the data at process block 2010.

It should be apparent to those skilled in the art that the example shownin FIG. 20 is not the only way to generate test patterns using multiplecomputers. For instance, the CUT design information may be stored on acomputer-readable medium that is not on a network and that is sentseparately to the server or computing environment (for example, aCD-ROM, DVD, or portable hard drive). Or, the server computer or remotecomputing environment may perform only a portion of the test patterngeneration procedure.

Having illustrated and described the principles of the disclosedtechnology, it will be apparent to those skilled in the art that thedisclosed embodiments can be modified in arrangement and detail withoutdeparting from such principles. In view of the many possibleembodiments, it will be recognized that the illustrated embodimentsinclude only examples and should not be taken as a limitation on thescope of the disclosed technology. Rather, the scope of the disclosedtechnology for purposes of this application is defined by the followingclaims and their equivalents. We therefore claim as our invention allthat comes within the scope and spirit of these claims and theirequivalents.

What is claimed is:
 1. A method of generating test patterns for testingan integrated circuit, comprising: identifying a fault that is detectedby a test pattern by simulating a response of an integrated circuitdesign to the test pattern in the presence of the fault and identifyingone or more paths that are sensitized by the test pattern and thatdetect the fault; computing a static path delay for a selectedsensitized path through the identified fault; determining whether acriterion based at least in part on the static path delay is met for theidentified fault; modifying a fault list by removing the identifiedfault if the criterion is met; and storing the modified fault list,wherein either: (a) the selected sensitized path is the longestsensitized path, and the act of determining whether the criterion is metcomprises determining whether:$\frac{T_{TC} - {PD}_{f}^{s}}{T_{TC}} \geq \lambda$ where PD_(f) ^(s) isthe static path delay through the longest sensitized path for the faultf, T_(TC) is the test clock period, and λ is a real number between 0 and1; or (b) wherein the selected sensitized path is the shortestsensitized path, and the act of determining whether the criterion is metcomprises determining whether:$\frac{T_{TC} - {HPD}_{f}^{s}}{T_{TC}} < \lambda$ where HPD_(f) ^(s) isthe static path delay through the shortest sensitized path for the faultf, T_(TC) is the test clock period, and λ is a real number between 0and
 1. 2. The method of claim 1, wherein the criterion is a firstcriterion, and wherein the method further comprises: computing an actualpath delay for the selected sensitized path through the identifiedfault; determining whether a second criterion based at least in part onthe actual path delay is met for the identified fault; and modifying thefault list by removing the identified fault if the first criterion isnot met but the second criterion is met.
 3. The method of claim 2,wherein the act of determining whether the second criterion is metcomprises determining whether:${\frac{{PD}_{f}^{s} - {PD}_{f}^{a}}{T_{TC} - {PD}_{f}^{a}} < \delta},$where PD_(f) ^(s) is the static path delay through the longestsensitized path for the fault f, PD_(f) ^(a) is the actual path delaythrough the longest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and
 1. 4. The method ofclaim 2, wherein the act of determining whether the second criterion ismet comprises determining whether:${\frac{{HPD}_{f}^{a} - {HPD}_{f}^{s}}{T_{TC} - {HPD}_{f}^{s}} < \delta},$where HPD_(f) ^(s) is the static path delay through the shortestsensitized path for the fault f, HPD_(f) ^(a) is the actual path delaythrough the shortest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and
 1. 5. The method ofclaim 1, wherein the method is repeated for additional faults in thefault list not detected by previously generated test patterns.
 6. One ormore non transitory computer-readable media storing computer-executableinstructions for causing a computer to perform a method, the methodcomprising: identifying a fault that is detected by a test pattern bysimulating a response of an integrated circuit design to the testpattern in the presence of the fault and identifying one or more pathsthat are sensitized by the test pattern and that detect the fault;computing a static path delay for a selected sensitized path through theidentified fault; determining whether a criterion based at least in parton the static path delay is met for the identified fault; modifying afault list by removing the identified fault if the criterion is met; andstoring the modified fault list, and wherein either: (a) the selectedsensitized path is the longest sensitized path, and the act ofdetermining whether the criterion is met comprises determining whether:$\frac{T_{TC} - {PD}_{f}^{s}}{T_{TC}} \geq \lambda$ where PD_(f) ^(s) isthe static path delay through the longest sensitized path for the faultf, T_(TC) is the test clock period, and λ is a real number between 0 and1; or (b) wherein the selected sensitized path is the shortestsensitized path, and the act of determining whether the criterion is metcomprises determining whether:$\frac{T_{TC} - {HPD}_{f}^{s}}{T_{TC}} < \lambda$ where HPD_(f) ^(s) isthe static path delay through the shortest sensitized path for the faultf, T_(TC) is the test clock period, and λ is a real number between 0and
 1. 7. One or more computer-readable media storing a fault listcreated by the method of claim
 6. 8. The one or more computer-readablemedia of claim 6, wherein the criterion is a first criterion, andwherein the method further comprises: computing an actual path delay forthe selected sensitized path through the identified fault; determiningwhether a second criterion based at least in part on the actual pathdelay is met for the identified fault; and modifying the fault list byremoving the identified fault if the first criterion is not met but thesecond criterion is met.
 9. The one or more computer-readable media ofclaim 8, wherein the act of determining whether the second criterion ismet comprises determining whether:${\frac{{PD}_{f}^{s} - {PD}_{f}^{a}}{T_{TC} - {PD}_{f}^{a}} < \delta},$where PD_(f) ^(s) is the static path delay through the longestsensitized path for the fault f, PD_(f) ^(a) is the actual path delaythrough the longest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and
 1. 10. The one ormore computer-readable media of claim 6, wherein the method is repeatedfor additional faults in the fault list not detected by previouslygenerated test patterns.
 11. The one or more computer-readable media ofclaim 8, wherein the act of determining whether the second criterion ismet comprises determining whether:${\frac{{HPD}_{f}^{a} - {HPD}_{f}^{s}}{T_{TC} - {HPD}_{f}^{s}} < \delta},$where HPD_(f) ^(s) is the static path delay through the shortestsensitized path for the fault f, HPD_(f) ^(a) is the actual path delaythrough the shortest sensitized path for the fault, T_(TC) is the testclock period, and δ is a real number between 0 and 1.